Publications by Michele Burrello
 2023

Quantum simulation of the tricritical Ising model in tunable Josephson
junction ladders 
Abstract
 Modern hybrid superconductorsemiconductor Josephson junction arrays are a promising platform for analog quantum simulations. Their controllable and nonsinusoidal energy/phase relation opens the path to implement nontrivial interactions and study the emergence of exotic quantum phase transitions. Here, we propose the analysis of an array of hybrid Josephson junctions defining a 2leg ladder geometry for the quantum simulation of the tricritical Ising phase transition. This transition provides the paradigmatic example of minimal conformal models beyond Ising criticality and its excitations are intimately related with Fibonacci nonAbelian anyons and topological order in two dimensions. We study this superconducting system and its thermodynamic phases based on bosonization and matrixproductstates techniques. Its effective continuous description in terms of a threefrequency sineGordon quantum field theory suggests the presence of the targeted tricritical point and the numerical simulations confirm this picture. Our results indicate which experimental observables can be adopted in realistic devices to probe the physics and the phase transitions of the model. Additionally, our proposal provides a useful onedimensional building block to design exotic topological order in twodimensional scalable Josephson junction arrays.
 2310.18300v2 [pdf]
Lorenzo Maffi, Niklas Tausendpfund, Matteo Rizzi, Michele Burrello [pdf]

The topological Kondo model out of equilibrium 
Abstract
 The topological Kondo effect is a genuine manifestation of the nonlocality of Majorana modes. We investigate its outofequilibrium signatures in a model with a Cooperpair box hosting four of these topological modes, each connected to a metallic lead. Through an advanced matrixproductstate approach tailored to study the dynamics of superconductors, we simulate the relaxation of the Majorana magnetization, which allows us to determine the related Kondo temperature, and we analyze the onset of electric transport after a quantum quench of a lead voltage. Our results apply to Majorana Cooperpair boxes fabricated in double nanowire devices and provide nonperturbative evidence of the crossover from weakcoupling states to the strongly correlated topological Kondo regime. The latter dominates at the superconductor charge degeneracy points and displays the expected universal fractional zerobias conductance.
 2307.03773v2 [pdf]
Matteo M. Wauters, ChiaMin Chung, Lorenzo Maffi, Michele Burrello [pdf]

Thouless pumping in Josephson junction arrays 
Abstract
 Recent advancements in fabrication techniques have enabled unprecedented clean interfaces and gate tunability in semiconductorsuperconductor heterostructures. Inspired by these developments, we propose protocols to realize Thouless quantum pumping in electrically tunable Josephson junction arrays. We analyze, in particular, the implementation of the RiceMele and the HarperHofstadter pumping schemes, whose realization would validate these systems as flexible platforms for quantum simulations. We investigate numerically the longtime behavior of chains of controllable superconducting islands in the Coulombblockaded regime. Our findings provide new insights into the dynamics of periodically driven interacting systems and highlight the robustness of Thouless pumping with respect to boundary effects typical of superconducting circuits.
 2308.13597v1 [pdf]
Stavros Athanasiou, Ida E. Nielsen, Matteo M. Wauters, Michele Burrello [pdf]

Strange correlators for topological quantum systems from bulkboundary correspondence 
Abstract
 "Strange" correlators provide a tool to detect topological phases arising in manybody models by computing the matrix elements of suitably defined twopoint correlations between the states under investigation and trivial reference states. Their effectiveness depends on the choice of the adopted operators. In this paper we give a systematic procedure for this choice, discussing the advantages of choosing operators using the bulkboundary correspondence of the systems under scrutiny. Via the scaling exponents, we directly relate the algebraic decay of the strange correlators with the scaling dimensions of gapless edge modes operators. We begin our analysis with lattice models hosting symmetryprotected topological phases and we analyze the sums of the strange correlators, pointing out that integrating their moduli substantially reduces cancellations and finitesize effects. We also analyze instances of systems hosting intrinsic topological order, as well as strange correlators between states with different nontrivial topologies. Our results for both translational and nontranslational invariant cases, and in presence of onsite disorder and longrange couplings, extend the validity of the strange correlators approach for the diagnosis of topological phases of matter, and indicate a general procedure for their optimal choice.
Luca Lepori, Michele Burrello, Andrea Trombettoni, Simone Paganelli Journal reference: Phys. Rev. B 108, 035110 (2023) [pdf] DOI: 10.1103/PhysRevB.108.035110

Simulations of the dynamics of quantum impurity problems with matrix
product states 
Abstract
 The Anderson impurity model is a paradigmatic example in the study of strongly correlated quantum systems and describes an interacting quantum dot coupled to electronic leads. In this work, we characterize the emergence of the Kondo effect by investigating the model dynamics following a quantum quench based on matrix product state simulations. The relaxation of the impurity magnetization allows for the estimate of the predicted universal scaling of the Kondo temperature as a function of the impuritylead hybridization and quantum dot repulsion. Additionally, our simulations permit us to evaluate the current in the nonequilibrium quasisteady state appearing after the quench. Through their values, we examine the dependence of the conductance on the voltage bias $V_b$ and on the impurity chemical potential $V_g$, which displays a zerobias Kondo peak. Our results are relevant for transport measurements in Coulomb blockaded devices, and, in particular, in quantum dots induced in nanowires.
 2304.13756v1 [pdf]
Matteo M. Wauters, ChiaMin Chung, Lorenzo Maffi, Michele Burrello [pdf]

Detecting Majorana modes by readout of poisoninginduced parity flips 
Abstract
 Reading out the parity degree of freedom of Majorana bound states is key to demonstrating their nonabelian exchange properties. Here, we present a lowenergy model describing localized edge states in a twoarm device. We study paritytocharge conversion based on coupling the superconductor bound states to a quantum dot whose charge is read out by a sensor. The dynamics of the system, including the readout device, is analyzed in full using a quantumjump approach. We show how the resulting signal and noise ratio differentiates between local Majorana and Andreev bound states.
Jens Schulenborg, Svend Krøjer, Michele Burrello, Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. B 107, L121401 (2023) [pdf] DOI: 10.1103/PhysRevB.107.L121401

Quantum simulation of the tricritical Ising model in tunable Josephson
junction ladders 
Abstract
 2022

Multiterminal transport spectroscopy of subgap states in Coulombblockaded superconductors 
Abstract
 Subgap states are responsible for the lowbias transport features of hybrid superconductingsemiconducting devices. Here, we analyze the local and nonlocal differential conductance of Coulombblockaded multiterminal superconducting islands that host subgap states with different spatial structures. The emerging patterns of their transport spectroscopy are used to characterize the possible topological nature of these devices and offer the possibility of controlling their transport properties. We develop a nexttoleading order master equation to describe the multiterminal transport in superconductors with both strong Coulomb interactions and multiple subgap states, coupled with metallic leads. We show that the nonlocal differential conductance characterizes the spatial extension of the subgap states and signals the presence of degenerate bound states with a finite support on different parts of the device. Additionally, it displays sharp sign changes as a function of the induced charge of the superconductor, signaling energy crossings among its lowest excited states.
Rubén Seoane Souto, Matteo M. Wauters, Karsten Flensberg, Martin Leijnse, Michele Burrello Journal reference: Phys. Rev. B 106, 235425 (2022) [pdf] DOI: 10.1103/PhysRevB.106.235425

Readout of Parafermionic States by Transport Measurements 
Abstract
 Recent experiments have demonstrated the possibility of inducing superconducting pairing into counterpropagating fractional quantum Hall edge modes. This paves the way for the realization of localized parafermionic modes, nonAbelian anyons that share fractional charges in a nonlocal way. We show that, for a pair of isolated parafermions, this joint degree of freedom can be read by conductance measurements across standard metallic electrodes. We propose two complementary setups. We investigate first the transport through a grounded superconductor hosting two interacting parafermions. In the lowenergy limit, its conductance peaks reveal their shared fractional charge yielding a threestate telegraph noise for weak quasiparticle poisoning. We then examine the twoterminal electron conductance of a blockaded fractional topological superconductor, which displays a characteristic $e/3$ periodicity of its zerobias peaks in the deep topological regime, thus signalling the presence of parafermionic modes.
Ida E. Nielsen, Karsten Flensberg, Reinhold Egger, Michele Burrello Journal reference: Phys. Rev. Lett. 129, 037703 (2022) [pdf] DOI: 10.1103/PhysRevLett.129.037703

TwoDimensional

Abstract
 We propose an implementation of a twodimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and twoqubits gates comparable to what can be achieved with presentday and nearfuture technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.
Luca Lumia, Pietro Torta, Glen B. Mbeng, Giuseppe E. Santoro, Elisa Ercolessi, Michele Burrello, Matteo M. Wauters [pdf] DOI: 10.1103/PRXQuantum.3.020320 2112.11787v2 [pdf]

Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices 
Abstract
 Superconducting devices subject to strong charging energy interactions and Coulomb blockade are one of the key elements for the development of nanoelectronics and constitute common building blocks of quantum computation platforms and topological superconducting setups. The study of their transport properties is nontrivial and some of their nonperturbative aspects are hard to capture with the most ordinary techniques. Here we present a matrix product state approach to simulate the realtime dynamics of these systems. We propose a study of their transport based on the analysis of the currents after quantum quenches connecting such devices with external leads. Our method is based on the combination of a Wilson chain construction for the leads and a meanfield BCS description for the superconducting scatterers. In particular, we employ a quasiparticle energy eigenbasis which greatly reduces their entanglement growth and we introduce an auxiliary degree of freedom to encode the device total charge. This approach allows us to treat nonperturbatively both their charging energy and coupling with external electrodes. We show that our construction is able to describe the Coulomb diamond structure of a superconducting dot with subgap states, including its sequential tunneling and cotunneling features. We also study the conductance zerobias peaks caused by Majorana modes in a blockaded Kitaev chain, and compare our results with common BreitWigner predictions.
ChiaMin Chung, Matteo M. Wauters, Michele Burrello Journal reference: Phys. Rev. B 106, 094308 (2022) [pdf] DOI: 10.1103/PhysRevB.106.094308

Electronic Transport in DoubleNanowire Superconducting Islands with Multiple Terminals 
Abstract
 We characterize insitu grown parallel nanowires bridged by a superconducting island. The magneticfield and temperature dependence of Coulomb blockade peaks measured across different pairs of nanowire ends are consistent with a subgap state extended over the hybrid parallelnanowire island. Being gatetunable, accessible by multiple terminals and free of quasiparticle poisoning, these nanowires show promise for the implementation of several proposals that rely on parallel nanowire platforms.
Alexandros Vekris, Juan Carlos Estrada Saldaña, Thomas Kanne, Thor HvidOlsen, Mikelis Marnauza, Dags Olsteins, Matteo M. Wauters, Michele Burrello, Jesper Nygård, Kasper GroveRasmussen [pdf] DOI: 10.1021/acs.nanolett.2c01161 2203.09213v1 [pdf]

Multiterminal transport spectroscopy of subgap states in Coulombblockaded superconductors 
Abstract
 2021

Van Hove singularities at phase transitions in topological metals 
Abstract
 We study 3D topological phase transitions between topological and trivial metals and we show that a subset of Van Hove (VH) singularities of the density of states sits exactly at the transition. We may refer to these as topological VH singularities. By investigating a minimal model, we show that they originate from energy saddle points located between Weyl points with opposite chiralities. We exemplify the relation between VH singularities and topological phase transitions in tightbinding Weyl systems by analysing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and understand the features of their density of states. In this model, as a function the magnetic flux, the occurrence of topological VH singularities can be explicitly checked.
 2106.05771v1 [pdf]
Pierpaolo Fontana, Michele Burrello, Andrea Trombettoni [pdf]

Multilevel effects in quantum dot based paritytocharge conversion of Majorana box qubits 
Abstract
 Quantumdot based paritytocharge conversion is a promising method for reading out quantum information encoded nonlocally into pairs of Majorana zero modes. To obtain a sizable paritytocharge visibility, it is crucial to tune the relative phase of the tunnel couplings between the dot and the Majorana modes appropriately. However, in the presence of multiple quasidegenerate dot orbitals, it is in general not experimentally feasible to tune all couplings individually. This paper shows that such configurations could make it difficult to avoid a destructive multiorbital interference effect that substantially reduces the readout visibility. We analyze this effect using a Lindblad quantum master equation. This exposes how the experimentally relevant system parameters enhance or suppress the visibility when strong charging energy, measurement dissipation and, most importantly, multiorbital interference is accounted for. In particular, we find that an intermediatetime readout could mitigate some of the interferencerelated visibility reductions affecting the stationary limit.
Jens Schulenborg, Michele Burrello, Martin Leijnse, Karsten Flensberg Journal reference: Phys. Rev. B 103, 245407 (2021) [pdf] DOI: 10.1103/PhysRevB.103.245407


Abstract
 Under the perspective of realizing analog quantum simulations of lattice gauge theories, ladder geometries offer an intriguing playground, relevant for ultracold atom experiments. Here, we investigate Hamiltonian lattice gauge theories defined in twoleg ladders. We consider a model that includes both gauge boson and Higgs matter degrees of freedom with local $\mathbb{Z}_N$ gauge symmetries. We study its phase diagram based on both an effective lowenergy field theory and density matrix renormalization group simulations. For $N\ge 5$, an extended gapless Coulomb phase emerges, which is separated by a BerezinskiiKosterlitzThouless phase transition from the surrounding gapped phase. Besides the traditional confined and Higgs regimes, we also observe a novel quadrupolar region, originated by the ladder geometry.
Jens Nyhegn, ChiaMin Chung, Michele Burrello Journal reference: Phys. Rev. Research 3, 013133 (2021) [pdf] DOI: 10.1103/PhysRevResearch.3.013133

Topological van Hove singularities at phase transitions in Weyl metals 
Abstract
 We show that in threedimensional (3D) topological metals, a subset of the van Hove singularities of the density of states sits exactly at the transitions between topological and trivial gapless phases. We may refer to these as topological van Hove singularities. By investigating two minimal models, we show that they originate from energy saddle points located between Weyl points with opposite chiralities, and we illustrate their topological nature through their magnetotransport properties in the ballistic regime. We exemplify the relation between van Hove singularities and topological phase transitions in Weyl systems by analyzing the 3D Hofstadter model, which offers a simple and interesting playground to consider different kinds of Weyl metals and to understand the features of their density of states. In this model, as a function of the magnetic flux, the occurrence of topological van Hove singularities can be explicitly checked.
Pierpaolo Fontana, Michele Burrello, Andrea Trombettoni Journal reference: Phys. Rev. B 104, 195127 (2021) [pdf] DOI: 10.1103/PhysRevB.104.195127

Van Hove singularities at phase transitions in topological metals 
Abstract
 2020

Exploring helical phases of matter in bosonic ladders 
Abstract
 Ladder models of ultracold atoms offer a versatile platform for the experimental and theoretical study of different phenomena and phases of matter linked to the interplay between artificial gauge fields and interactions. Strongly correlated helical states are known to appear for specific ratios of the particle and magnetic flux densities and they can often be interpreted as a onedimensional limit of fractional quantum Hall states, thus being called pretopological. Their signatures, however, are typically hard to observe due to the small gaps characterizing these states. Here we investigate bosonic ladder models at filling factor 1. Based on bosonization, renormalization group and matrix product state simulations we pinpoint two strongly correlated helical phases appearing at this resonance. We show that one of them can be accessed in systems with twospecies hardcore bosons and onsite repulsions only, thus amenable for optical lattice experiments. Its signatures are sizable and stable over a broad range of parameters for realistic system sizes.
Andreas Haller, Apollonas S. MatsoukasRoubeas, Yueting Pan, Matteo Rizzi, Michele Burrello Journal reference: Phys. Rev. Research 2, 043433 (2020) [pdf] DOI: 10.1103/PhysRevResearch.2.043433

Reaching the quantum Hall regime with rotating Rydbergdressed atoms 
Abstract
 Despite the striking progress in the field of quantum gases, one of their much anticipated application  the simulation of quantum Hall states  remains elusive: all experimental approaches so far failed in reaching a sufficiently small ratio between atom and vortex densities. In this paper we consider rotating Rydbergdressed atoms in magnetic traps: these gases offer strong and tunable nonlocal repulsive interactions and very low densities; hence they provide an exceptional platform to reach the quantum Hall regime. Based on the Lindemann criterion and the analysis of the interplay of the length scales of the system, we show that there exists an optimal value of the dressing parameters that minimizes the ratio between the filling factor of the system and its critical value to enter the Hall regime, thus making it possible to reach this stronglycorrelated phase for more than 1000 atoms under realistic conditions.
Michele Burrello, Igor Lesanovsky, Andrea Trombettoni Journal reference: Phys. Rev. Research 2, 023290 (2020) [pdf] DOI: 10.1103/PhysRevResearch.2.023290

Exploring helical phases of matter in bosonic ladders 
Abstract
 2019

Springer Proceedings in Physics 
Abstract
 We discuss and review in this chapter the developing field of research of quantum simulation of gauge theories with ultracold atoms.
João C. Pinto Barros, Michele Burrello, Andrea Trombettoni [pdf] DOI: 10.1007/9783030354732 1911.06022v1 [pdf]

Field theory approach to the quantum transport in Weyl semimetals 
Abstract
 We analyze the structure of the surface states and Fermi arcs of Weyl semimetals as a function of the boundary conditions parameterizing the Hamiltonian selfadjoint extensions of a minimal model with two Weyl points. These boundary conditions determine both the pseudospin polarization of the system on the surface and the shape of the associated Fermi arcs. We analytically derive the expectation values of the density profile of the surface current, we evaluate the anomalous Hall conductivity as a function of temperature and chemical potential and we discuss the surface current correlation functions and their contribution to the thermal noise. Based on a lattice variant of the model, we numerically study the surface states at zero temperature and we show that their polarization and, consequently, their transport properties, can be varied by suitable Zeeman terms localized on the surface. We also provide an estimate of the bulk conductance of the system based on the LandauerB\"uttiker approach. Finally, we analyze the surface anomalous thermal Hall conductivity and we show that the boundary properties lead to a correction of the expected universal thermal Hall conductivity, thus violating the WiedemannFranz law.
Michele Burrello, Enore Guadagnini, Luca Lepori, Mihail Mintchev Journal reference: Phys. Rev. B 100, 155131 (2019) [pdf] DOI: 10.1103/PhysRevB.100.155131

Coulombinteractioninduced Majorana edge modes in nanowires 
Abstract
 We show that Majorana edge modes appear in a strongly correlated phase of semiconducting nanowires with discrete rotational symmetry in the cross section. These modes exist in the absence of spinorbit coupling, magnetic fields and superconductivity. They appear purely due to the combination of the threedimensional Coulomb interaction and orbital physics, which generates a fermionic condensate exhibiting a topological ground state degeneracy in a sector of the spectrum which is gapped to continuum modes. The gap can be comparable in magnitude to the topological superconducting gap in other solidstate candidate systems for Majorana edge modes, and may similarly be probed via tunnel spectroscopy.
Tommy Li, Michele Burrello, Karsten Flensberg Journal reference: Phys. Rev. B 100, 045305 (2019) [pdf] DOI: 10.1103/PhysRevB.100.045305

Springer Proceedings in Physics 
Abstract
 2018

Dyonic zeroenergy modes 
Abstract
 Onedimensional systems with topological order are intimately related to the appearance of zeroenergy modes localized on their boundaries. The most common example is the Kitaev chain, which displays Majorana zeroenergy modes and it is characterized by a twofold ground state degeneracy related to the global $\mathbb{Z}_2$ symmetry associated with fermionic parity. By extending the symmetry to the $\mathbb{Z}_N$ group, it is possible to engineer systems hosting topological parafermionic modes. In this work, we address onedimensional systems with a generic discrete symmetry group $G$. We define a ladder model of gauge fluxes that generalizes the Ising and Potts models and displays a symmetry broken phase. Through a nonAbelian JordanWigner transformation, we map this flux ladder into a model of dyonic operators, defined by the group elements and irreducible representations of $G$. We show that the soobtained dyonic model has topological order, with zeroenergy modes localized at its boundary. These dyonic zeroenergy modes are in general weak topological modes, but strong dyonic zero modes appear when suitable positiondependent couplings are considered.
Morten I. K. Munk, Asbjørn Rasmussen, Michele Burrello Journal reference: Phys. Rev. B 98, 245135 (2018) [pdf] DOI: 10.1103/PhysRevB.98.245135

Axial anomaly in multiWeyl and triplepoint semimetals 
Abstract
 We derive the expression of the abelian axial anomaly in the socalled multiWeyl and triplepoint crossing semimetals. No simplifying restrictions are assumed on the symmetry of the spectrum. Three different computation methods are considered: the perturbative quantum field theory procedure which is based on the evaluation of the oneloop Feynman diagrams, the NielsenNinomiya method, and the AtiyahSinger index argument. It is shown that the functional form of the axial anomaly does not depend on the Lorentz symmetry, but it is determined by the gauge structure group. We discuss the stability of the anomaly  stemming from the quantisation of the anomaly coefficient  under smooth modifications of the lagrangian parameters.
Luca Lepori, Michele Burrello, Enore Guadagnini Journal reference: J. High En. Phys. (2018) [pdf] DOI: 10.1007/JHEP06(2018)110

The resonant state at filling factor

Abstract
 Helical liquids have been experimentally detected in both nanowires and ultracold atomic chains as the result of strong spinorbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as synthetic ladders, with artificial magnetic fluxes determined by the spinorbit terms. In this work, we characterize the helical state which appears at filling $\nu=1/2$: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the onedimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlinlike states.
A. Haller, M. Rizzi, M. Burrello Journal reference: New J. Phys. 20 (2018) 053007 [pdf] DOI: 10.1088/13672630/aab8d4

Geometrically protected triplepoint crossings in an optical lattice 
Abstract
 We show how to realize topologically protected crossings of three energy bands, integerspin analogs of Weyl fermions, in threedimensional optical lattices. Our proposal only involves ultracold atom techniques that have already been experimentally demonstrated and leads to isolated triplepoint crossings (TPCs) which are required to exist by a novel combination of lattice symmetries. The symmetries also allow for a new type of topological object, the typeII, or tilted, TPC. Our Rapid Communication shows that spin1 Weyl points, which have not yet been observed in the bandstructure of crystals, are within reach of ultracold atom experiments.
I. C. Fulga, L. Fallani, M. Burrello Journal reference: Phys. Rev. B 97, 121402 (2018) [pdf] DOI: 10.1103/PhysRevB.97.121402

Dyonic zeroenergy modes 
Abstract
 2017

Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant nonAbelian potentials 
Abstract
 We present a general analytical formalism to determine the energy spectrum of a quantum particle in a cubic lattice subject to translationally invariant commensurate magnetic fluxes and in the presence of a general spaceindependent nonAbelian gauge potential. We first review and analyze the case of purely Abelian potentials, showing also that the socalled Hasegawa gauge yields a decomposition of the Hamiltonian into submatrices having minimal dimension. Explicit expressions for such matrices are derived, also for general anisotropic fluxes. Later on, we show that the introduction of a translational invariant nonAbelian coupling for multicomponent spinors does not affect the dimension of the minimal Hamiltonian blocks, nor the dimension of the magnetic Brillouin zone. General formulas are presented for the U(2) case and explicit examples are investigated involving $\pi$ and $2\pi/3$ magnetic fluxes. Finally, we numerically study the effect of random flux perturbations.
M. Burrello, I. C. Fulga, L. Lepori, A. Trombettoni Journal reference: J. Phys. A: Math. Theor. 50, 455301 (2017) [pdf] DOI: 10.1088/17518121/aa8d26

Abelian gauge potentials on cubic lattices 
Abstract
 The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold setups, we study cubic lattice tightbinding models with commensurate flux. We finally examine applications of gauge potentials in onedimensional rings.
 1706.02228v1 [pdf]
Michele Burrello, Luca Lepori, Simone Paganelli, Andrea Trombettoni [pdf]

Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant nonAbelian potentials 
Abstract
 2016

Double Weyl points and Fermi arcs of topological semimetals in nonAbelian gauge potentials 
Abstract
 We study the effect of a nonAbelian SU(2) gauge potential on the topological semimetal induced by a magnetic field having {\pi}flux per plaquette and acting on fermions in a cubic lattice. The Abelian {\pi}flux term gives rise to a spectrum characterized by Weyl points. When the nonAbelian part is turned on, due to the presence of a C4 rotation symmetry, the Weyl points assume a quadratic dispersion along two directions and constitute double monopoles for the Berry curvature. We examine both analytically and numerically the main features of this system, focusing on its gapless surface modes, the socalled Fermi arcs. We discuss the stability of the system under confining hardwall and harmonic potentials, relevant for the implementation in ultracold atom settings, and the effect of rotation symmetry breaking.
Luca Lepori, Ion Cosma Fulga, Andrea Trombettoni, Michele Burrello Journal reference: Phys. Rev. A 94, 053633 (2016) [pdf] DOI: 10.1103/PhysRevA.94.053633

Projected Entangled Pair States with nonAbelian gauge symmetries: An SU(2) study 
Abstract
 Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a nonAbelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both twocolor fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.
Erez Zohar, Thorsten B. Wahl, Michele Burrello, J. Ignacio Cirac Journal reference: Ann. Phys 374, 84137 (2016) [pdf] DOI: 10.1016/j.aop.2016.08.008


Abstract
 Weyl semimetals typically appear in systems in which either timereversal (T) or inversion (P}) symmetry are broken. Here we show that in the presence of gauge potentials these topological states of matter can also arise in fermionic lattices preserving both T and P. We analyze in detail the case of a cubic lattice model with $\pi$fluxes, discussing the role of gauge symmetries in the formation of Weyl points and the difference between the physical and the canonical T and P symmetries. Motivated by advances in ultracold atom experiments and by the possibility of using synthetic magnetic fields, we examine the robustness of the Weyl semimetal phase in the presence of trapping potentials and random perturbations of the magnetic fluxes, which can be compared to a local disorder in realistic scenarios.
L. Lepori, I. C. Fulga, A. Trombettoni, M. Burrello Journal reference: Phys. Rev. B 94, 085107 (2016) [pdf] DOI: 10.1103/PhysRevB.94.085107

Building projected entangled pair states with a local gauge symmetry 
Abstract
 Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.
Erez Zohar, Michele Burrello Journal reference: New J. Phys. 18, 043008 (2016) [pdf] DOI: 10.1088/13672630/18/4/043008

Double Weyl points and Fermi arcs of topological semimetals in nonAbelian gauge potentials 
Abstract
 2015

Fermionic projected entangled pair states and local

Abstract
 Tensor networks, and in particular Projected Entangled Pair States (PEPS), are a powerful tool for the study of quantum many body physics, thanks to both their builtin ability of classifying and studying symmetries, and the efficient numerical calculations they allow. In this work, we introduce a way to extend the set of symmetric PEPS in order to include local gauge invariance and investigate lattice gauge theories with fermionic matter. To this purpose, we provide as a case study and first example, the construction of a fermionic PEPS, based on Gaussian schemes, invariant under both global and local U(1) gauge transformations. The obtained states correspond to a truncated U(1) lattice gauge theory in 2 + 1 dimensions, involving both the gauge field and fermionic matter. For the global symmetry (pure fermionic) case, these PEPS can be studied in terms of spinless fermions subject to a pwave superconducting pairing. For the local symmetry (fermions and gauge fields) case, we find confined and deconfined phases in the pure gauge limit, and we discuss the screening properties of the phases arising in the presence of dynamical matter.
Erez Zohar, Michele Burrello, Thorsten B. Wahl, J. Ignacio Cirac Journal reference: Annals of Physics (2015), pp. 385439 [pdf] DOI: 10.1016/j.aop.2015.10.009

Methods for detecting charge fractionalization and winding numbers in an interacting fermionic ladder 
Abstract
 We consider a spin1/2 fermionic ladder with spinorbit coupling and a perpendicular magnetic field, which shares important similarities with topological superconducting wires. We fully characterize the symmetryprotected topological phase of this ladder through the identification of fractionalized edge modes and nontrivial spin winding numbers. We propose an experimental scheme to engineer such a ladder system with cold atoms in optical lattices, and we present two protocols that can be used to extract the topological signatures from density and momentumdistribution measurements. We then consider the presence of interactions and discuss the effects of a contact onsite repulsion on the topological phase. We find that such interactions could enhance the extension of the topological phase in certain parameters regimes.
Leonardo Mazza, Monika Aidelsburger, HongHao Tu, Nathan Goldman, Michele Burrello Journal reference: New J. Phys. 17 (2015) 105001 [pdf] DOI: 10.1088/13672630/17/10/105001

Formulation of lattice gauge theories for quantum simulations 
Abstract
 We examine the KogutSusskind formulation of lattice gauge theories under the light of fermionic and bosonic degrees of freedom that provide a description useful to the development of quantum simulators of gauge invariant models. We consider both discrete and continuous gauge groups and adopt a realistic multicomponent Fock space for the definition of matter degrees of freedom. In particular, we express the Hamiltonian of the gauge theory and the Gauss law in terms of Fock operators. The gauge fields are described in two different bases, based on either group elements or group representations. This formulation allows for a natural scheme to achieve a consistent truncation of the Hilbert space for continuous groups, and provides helpful tools to study the connections of gauge theories with topological quantum double and stringnet models for discrete groups. Several examples, including the case of the discrete $D_3$ gauge group, are presented.
Erez Zohar, Michele Burrello Journal reference: Phys. Rev. D 91, 054506 (2015) [pdf] DOI: 10.1103/PhysRevD.91.054506

Strongly correlated states of trapped ultracold fermions in deformed Landau levels 
Abstract
 We analyze the strongly correlated regime of a twocomponent trapped ultracold fermionic gas in a synthetic nonAbelian U(2) gauge potential, that consists of both a magnetic field and a homogeneous spinorbit coupling. This gauge potential deforms the Landau levels (LLs) with respect to the Abelian case and exchanges their ordering as a function of the spinorbit coupling. In view of experimental realizations, we show that a harmonic potential combined with a Zeeman term, gives rise to an angular momentum term, which can be used to test the stability of the correlated states obtained through interactions. We derive the Haldane pseudopotentials (HPs) describing the interspecies contact interaction within a lowest LL approximation. Unlike ordinary fractional quantum Hall systems and ultracold bosons with shortrange interactions in the same gauge potential, the HPs for sufficiently strong nonAbelian fields show an unconventional nonmonotonic behaviour in the relative angular momentum. Exploiting this property, we study the occurrence of new incompressible ground states as a function of the total angular momentum. In the first deformed Landau level (DLL) we obtain Laughlin and Jain states. Instead, in the second DLL three classes of stabilized states appear: Laughlin states, a series of intermediate strongly correlated states and finally vortices of the integer quantum Hall state. Remarkably, in the intermediate regime, the nonmonotonic HPs of the second DLL induce twoparticle correlations which are reminiscent of paired states such as the Haffnian state. Via exact diagonalization in the disk geometry, we compute experimentally relevant observables such as density profiles and correlations, and we study the entanglement spectra as a further tool to characterize the obtained strongly correlated states.
M. Burrello, M. Rizzi, M. Roncaglia, A. Trombettoni Journal reference: Phys. Rev. B 91, 115117 (2015) [pdf] DOI: 10.1103/PhysRevB.91.115117

Fermionic projected entangled pair states and local

Abstract
 2014

Commensurate and incommensurate states of topological quantum matter 
Abstract
 We prove numerically and by dualities the existence of modulated, commensurate and incommensurate states of topological quantum matter in simple systems of parafermions, motivated by recent proposals for the realization of such systems in mesoscopic arrays. In two space dimensions, we obtain the simplest representative of a topological universality class that we call Lifshitz. It is characterized by a topological tricritical point where a nonlocally ordered homogeneous phase meets a disordered phase and a third phase that displays modulations of a nonlocal order parameter.
Ashley Milsted, Emilio Cobanera, Michele Burrello, Gerardo Ortiz Journal reference: Phys. Rev. B 90, 195101 (2014) [pdf] DOI: 10.1103/PhysRevB.90.195101

Commensurate and incommensurate states of topological quantum matter 
Abstract
 2013

Topological phase transitions driven by nonAbelian gauge potentials in optical square lattices 
Abstract
 We analyze a tightbinding model of ultracold fermions loaded in an optical square lattice and subjected to a synthetic nonAbelian gauge potential featuring both a magnetic field and a translationally invariant SU(2) term. We consider in particular the effect of broken timereversal symmetry and its role in driving nontrivial topological phase transitions. By varying the spinorbit coupling parameters, we find both a semimetal/insulator phase transition and a topological phase transition between insulating phases with different numbers of edge states. The spin is not a conserved quantity of the system and the topological phase transitions can be detected by analyzing its polarization in time of flight images, providing a clear diagnostic for the characterization of the topological phases through the partial entanglement between spin and lattice degrees of freedom.
M. Burrello, I. C. Fulga, E. Alba, L. Lepori, A. Trombettoni Journal reference: Phys. Rev. A 88, 053619 (2013) [pdf] DOI: 10.1103/PhysRevA.88.053619

Effects of disorder on Coulombassisted braiding of Majorana zero modes 
Abstract
 Majorana zero modes in onedimensional topological superconductors obey nonAbelian braiding statistics. Braiding manipulations can be realized by controlling Coulomb couplings in hybrid Majoranatransmon devices. However, strong disorder may induce accidental Majorana modes, which are expected to have detrimental effects on braiding statistics. Nevertheless, we show that the Coulombassisted braiding protocol is efficiently realized also in the presence of accidental modes. The errors occurring during the braiding cycle are small if the couplings of the computational Majorana modes to the accidental ones are much weaker than the maximum Coulomb coupling.
I. C. Fulga, B. van Heck, M. Burrello, T. Hyart Journal reference: Phys. Rev. B 88, 155435 (2013) [pdf] DOI: 10.1103/PhysRevB.88.155435

Fluxcontrolled quantum computation with Majorana fermions 
Abstract
 Majorana fermions hold promise for quantum computation, because their nonAbelian braiding statistics allows for topologically protected operations on quantum information. Topological qubits can be constructed from pairs of wellseparated Majoranas in networks of nanowires. The coupling to a superconducting charge qubit in a transmission line resonator (transmon) permits braiding of Majoranas by external variation of magnetic fluxes. We show that readout operations can also be fully fluxcontrolled, without requiring microscopic control over tunnel couplings. We identify the minimal circuit that can perform the initializationbraidingmeasurement steps required to demonstrate nonAbelian statistics. We introduce the Random Access Majorana Memory, a scalable circuit that can perform a joint parity measurement on Majoranas belonging to a selection of topological qubits. Such multiqubit measurements allow for the efficient creation of highly entangled states and simplify quantum error correction protocols by avoiding the need for ancilla qubits.
T. Hyart, B. van Heck, I. C. Fulga, M. Burrello, A. R. Akhmerov, C. W. J. Beenakker Journal reference: Phys. Rev. B 88, 035121 (2013) [pdf] DOI: 10.1103/PhysRevB.88.035121

Topological phases in twodimensional arrays of parafermionic zero modes 
Abstract
 It has recently been realized that zero modes with projective nonAbelian statistics, generalizing the notion of Majorana bound states, may exist at the interface between a superconductor and a ferromagnet along the edge of a fractional topological insulator (FTI). Here we study twodimensional architectures of these nonAbelian zero modes, whose interactions are generated by the charging and Josephson energies of the superconductors. We derive lowenergy Hamiltonians for two different arrays of FTIs on the plane, revealing an interesting interplay between the realspace geometry of the system and its topological properties. On the one hand, in a geometry where the length of the FTI edges is independent on the system size, the array has a topologically ordered phase, giving rise to a qudit toric code Hamiltonian in perturbation theory. On the other hand, in a geometry where the length of the edges scales with system size, we find an exact duality to an Abelian lattice gauge theory and no topological order.
Michele Burrello, Bernard van Heck, Emilio Cobanera Journal reference: Phys. Rev. B 87, 195422 (2013) [pdf] DOI: 10.1103/PhysRevB.87.195422

Braiding of nonAbelian anyons using pairwise interactions 
Abstract
 The common approach to topological quantum computation is to implement quantum gates by adiabatically moving nonAbelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a Tjunction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.
M. Burrello, B. van Heck, A. R. Akhmerov Journal reference: Phys. Rev. A 87, 022343 (2013) [pdf] DOI: 10.1103/PhysRevA.87.022343

Topological Blockade and Measurement of Topological Charge 
Abstract
 The fractionally charged quasiparticles appearing in the 5/2 fractional quantum Hall plateau are predicted to have an extra nonlocal degree of freedom, known as topological charge. We show how this topological charge can block the tunnelling of these particles, and how such 'topological blockade' can be used to readout their topological charge. We argue that the short time scale required for this measurement is favorable for the detection of the nonAbelian anyonic statistics of the quasiparticles. We also show how topological blockade can be used to measure braiding statistics, and to couple a topological qubit with a conventional one.
B. van Heck, M. Burrello, A. Yacoby, A. R. Akhmerov Journal reference: Phys. Rev. Lett. 110, 086803 (2013) [pdf] DOI: 10.1103/PhysRevLett.110.086803

Fractional quantum Hall states of a Bose gas with a spin–orbit coupling 
Abstract
 We study the fractional quantum Hall phases of a pseudospin1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field also mimics an intrinsic spinorbit coupling of the Rashba type. While the spin degeneracy of the Landau levels is lifted by the spinorbit coupling, the crossing of two Landau levels at certain coupling strengths gives rise to a new degeneracy. We therefore take into account two Landau levels, and perform exact diagonalization of the manybody Hamiltonian. We study and characterize the quantum Hall phases which occur in the vicinity of the degeneracy point. Notably, we describe the different states appearing at the Laughlin filling, \nu=1/2. While for this filling incompressible phases disappear at the degeneracy point, denser systems at \nu=3/2 and \nu=2 are found to be clearly gapped. For filling factors \nu=2/3 and \nu=4/3, we discuss the connection of the exact ground state to the nonAbelian spin singlet states, obtained as the ground state of k+1 body contact interactions.
T. Grass, B. JuliáDíaz, M. Burrello, M. Lewenstein Journal reference: J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 134006 [pdf] DOI: 10.1088/09534075/46/13/134006

Topological phase transitions driven by nonAbelian gauge potentials in optical square lattices 
Abstract
 2012

Coulombassisted braiding of Majorana fermions in a Josephson junction array 
Abstract
 We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are chargeneutral quasiparticles (equal to their own antiparticle), they have an effective longrange interaction through the evenodd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the nonAbelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor.
B. van Heck, A. R. Akhmerov, F. Hassler, M. Burrello, C. W. J. Beenakker Journal reference: New J. Phys. 14, 035019 (2012) [pdf] DOI: 10.1088/13672630/14/3/035019

Coulombassisted braiding of Majorana fermions in a Josephson junction array 
Abstract
 2011

Ultracold atoms in U(2) nonAbelian gauge potentials preserving the Landau levels 
Abstract
 We study ultracold atoms subjected to U(2) nonAbelian potentials: we consider gauge potentials having, in the Abelian limit, degenerate Landau levels and we then investigate the effect of general homogeneous nonAbelian terms. The conditions under which the structure of degenerate Landau levels is preserved are classified and discussed. The typical gauge potentials preserving the Landau levels are characterized by a fictitious magnetic field and by an effective spinorbit interaction, e.g. obtained through the rotation of twodimensional atomic gases coupled with a tripod scheme. The singleparticle energy spectrum can be exactly determined for a class of gauge potentials, whose physical implementation is explicitly discussed. The corresponding Landau levels are deformed by the nonAbelian contribution of the potential and their spin degeneracy is split. The related deformed quantum Hall states for fermions and bosons (in the presence of strong intraspecies interaction) are determined far from and at the degeneracy points of the Landau levels. A discussion of the effect of the angular momentum is presented, as well as results for U(3) gauge potentials.
Michele Burrello, Andrea Trombettoni Journal reference: Phys. Rev. A 84, 043625 (2011) [pdf] DOI: 10.1103/PhysRevA.84.043625

Ultracold atoms in U(2) nonAbelian gauge potentials preserving the Landau levels 
Abstract
 2010

NonAbelian Anyons from Degenerate Landau Levels of Ultracold Atoms in Artificial Gauge Potentials 
Abstract
 We show that nonabelian potentials acting on ultracold gases with two hyperfine levels can give rise to ground states with nonabelian excitations. We consider a realistic gauge potential for which the Landau levels can be exactly determined: the nonabelian part of the vector potential makes the Landau levels nondegenerate. In the presence of strong repulsive interactions, deformed Laughlin ground states occur in general. However, at the degeneracy points of the Landau levels, nonabelian quantum Hall states appear: these ground states, including deformed MooreRead states (characterized by Ising anyons as quasiholes), are studied for both fermionic and bosonic gases.
Michele Burrello, Andrea Trombettoni Journal reference: Phys.Rev.Lett.105:125304,2010 [pdf] DOI: 10.1103/PhysRevLett.105.125304

Topological quantum gate construction by iterative pseudogroup hashing 
Abstract
 We describe the hashing technique to obtain a fast approximation of a target quantum gate in the unitary group SU(2) represented by a product of the elements of a universal basis. The hashing exploits the structure of the icosahedral group [or other finite subgroups of SU(2)] and its pseudogroup approximations to reduce the search within a small number of elements. One of the main advantages of the pseudogroup hashing is the possibility to iterate to obtain more accurate representations of the targets in the spirit of the renormalization group approach. We describe the iterative pseudogroup hashing algorithm using the universal basis given by the braidings of Fibonacci anyons. The analysis of the efficiency of the iterations based on the random matrix theory indicates that the runtime and the braid length scale polylogarithmically with the final error, comparing favorably to the SolovayKitaev algorithm.
Michele Burrello, Giuseppe Mussardo, Xin Wan [pdf] DOI: 10.1088/13672630/13/2/025023 1009.5808v1 [pdf]

Topological Quantum Hashing with the Icosahedral Group 
Abstract
 We study an efficient algorithm to hash any single qubit gate (or unitary matrix) into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of randommatrix representations of braids. With braids of length O[log(1/epsilon)], we can approximate all SU(2) matrices to an average error epsilon with a cost of O[log(1/epsilon)] in time. The algorithm is applicable to generic quantum compiling.
Michele Burrello, Haitan Xu, Giuseppe Mussardo, Xin Wan Journal reference: Phys.Rev.Lett.104:160502,2010 [pdf] DOI: 10.1103/PhysRevLett.104.160502

NonAbelian Anyons from Degenerate Landau Levels of Ultracold Atoms in Artificial Gauge Potentials 
Abstract
 2008

Quantum Field Theory on Star Graphs 
Abstract
 We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the fourfermion bulk interaction in detail. Using bosonization and vertex operators, we solve the model exactly for scale invariant boundary conditions, formulated in terms of the fermion current and without dissipation. The critical points are classified and determined explicitly. These results are applied for deriving the charge and spin transport, which have interesting physical features.
B. Bellazzini, M. Burrello, M. Mintchev, P. Sorba [pdf]

Quantum Field Theory on Star Graphs 
Abstract